Question 200410
Keiko bicycles 4 km/h faster than javier. 
In the same time it takes Javier to bicycle 30 km, Keiki can bicycle 42 km.
 How fast does each bicyclist travel?
;
Let s = j's speed
then
(s+4) = k's speed
:
Write a time equation, Time = {{{dist/speed}}}
:
k's time = j's time
{{{42/((s+4))}}} = {{{30/s}}}
Cross multiply
42s = 30(s+4)
42s = 30s + 120
42x - 30s = 120
12s = 120
 s = {{{120/12}}}
 s = 10 km/hr is j's speed
and
10 + 4 = 14 km/hr is k' speed
:
;
Check solution by finding the times:
42/14 = 3 hrs
30/10 = 3 hrs, confirms our solutions